An Introduction to the Mathematics of Biology: With Computer Algebra Models
This text has been adopted at: Georgia Institute of Technology, Carnegie Mellon University, University of California at Los Angeles, California State University, Northeastern Illinois University, and University of Colorado. The authors of this new textbook have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another but has a unity of its own. The biology and mathematics are equal; they are complete and flow smoothly into and out of one another. Student response to this approach has been exhilarating to watch as standard, unexciting applications give way to problems of contemporary interest- HIV, genetics and aging, for example. The book has several important features that the authors have developed from their classroom experience. First and foremost, it is designed to be comprehensible to students of biology as well as to students of mathematics and related physical sciences. No prior study of biology is necessary and only a year of calculus is required. The mathematics proceeds from simple to more complex concepts, and the biology proceeds from the population level down to the molecular level. This arrangement makes the material accessible to most biology majors and to most mathematics students near the beginning of their mathematical studies. A unique feature of the book is the use of a computer algebra system, Maple, in parts of every chapter. This hands-on approach to computation provides a rich source of information through the use of 'what-if' scenarios and thus allows students to grasp important biological and mathematical concepts in a way that is not possible without such technology. For students who do not have access to a computer algebra system, each topic is complete without the use of either numerical or symbolic equations. Graphic visualizations are provided for all the mathematical results. The text has extensive exercises, problems and examples, along with references for further study. It will be of interest to any mathematics department that teaches mathematical biology. It also lends itself to self-study for more advanced mathematicians and scientists who wish to explore further this most exciting frontier in the applications of mathematics and computers to the natural sciences. CONTENTS: Preface Acknowledgements Biology, Mathematics and a Mathematical Biology Laboratory Some Mathematical Tools Reproduction and the Drive for Survival Interactions Between Organisms and Their Environment Age-Dependent Population Structures Random Movements in Space and Time The Biological Disposition of Drugs and Inorganic Toxins Neurophysiology The Biochemistry of Cells A Biomathematical Approach to HIV and AIDS Genetics Index
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Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens
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